CN101677764A - A method for determining insulin sensitivity and glucose absorption - Google Patents

Abstract

The present invention encompasses a model-based method for determining insulin sensitivity and glucose absorption from oral glucose tolerance tests or mixed meals. The present invention has several advantages over current methods. The technique requires about four to six blood samples taken over about two to three hours following glucose ingestion and is therefore applicable to large-scale clinical trials. The analysis involves a reduced version of the classical minimal model, a method for describing glucose absorption using only two parameters, and an integral approach enabling the parametersto be obtained using simple algebra. The present method robustly identifies differences in insulin sensitivity in different patient types as well as improvements in insulin sensitivity arising from pharmaceutic therapy. In addition, insulin sensitivity measurements obtained with the present method are highly correlated with results from hyperinsulinemic clamps (r<2>>0.8). This method is thereforea practical and robust method for determining insulin sensitivity under physiologic conditions.

Description

Be used to measure the method for insulin sensitivity and glucose absorption

CROSS-REFERENCE TO RELATED PATENT

The present patent application requirement is 60/912 respectively at the serial number that the name of submitting on April 20th, 2007 and on October 16th, 2007 is called " A Method for Determining Insulin Sensitivity andGlucose Absorption (being used to measure the method for insulin sensitivity and glucose absorption) ", the priority of 998 and 60/980,230 U.S. Provisional Patent Application.

Background technology

Insulin resistance is the characteristic properties that comprises the multiple metabolic disease of obesity, type 2 diabetes mellitus and metabolism syndrome.Before this, developed some kinds of methods and measured insulin sensitivity based on empty stomach measurement, glucose tolerance test or euglycemia-Gao blood insulin pincers.Referring to for example 5122362.

The insulin sensitivity of measuring the patient with the improvement of the insulin sensitivity that quantizes different therapy and realized, differentiate that the insulin sensitivity in the individuality is very attracting with their pathophysiology of further understanding and definite optimal treatment method and the change of differentiating insulin sensitivity as the early stage labelling of disease progression.In addition, because similar reason to measure insulin sensitivity in preclinical study also quite attractive.

Recently, proposed from the several method of oral glucose tolerance test (OGTT) and meals test determination insulin sensitivity.A kind of method relates to the program that comprises two steps, and wherein tracer is used to measure the speed of glucose absorption, and then classical least model analytic process is used to measure insulin sensitivity.The test difficulty relevant with this method makes it not be suitable for large-scale research.People such as DallaMan (2005a) have developed a kind of method, are used to bring out from meals seven parts or more parts of definite simultaneously parameters of describing glucose absorption and insulin sensitivity of blood sample of (mealchallenge) and OGTT.In the non-diabetic experimenter this method is contrasted multiple tracing method and verify, the results relevance of result and high blood insulin pincers is good.People (2005b) such as Dalla Man.Yet this method needs at least seven parts of blood samples and has and the as many parameter of data point of gathering has to be determined.In addition, also need sophisticated simulation softward and do not guarantee to find single optimal solution.People such as Caumo (2000) by hypothesis on the feed during glucose absorption speed follow plasma glucose concentration closely, and duration sufficient to guarantee concentration of glucose and insulin action all returned to basic value during equation is carried out integration and derives insulin sensitivity sex index.

Other more experimental methods of insulin sensitivity have also been proposed to measure from OGTT.People such as stumvoll (2000) have obtained insulin sensitivity empirically and have measured based on glucose that records during OGTT and insulin measured value, this measure with high blood insulin pincers during glucose infusion speed relevant.People such as Matsuda (1999) have been developed a kind of compound insulin sensitivity based on the meansigma methods of the empty stomach value of glucose and insulin and glucose and insulin and have been measured, and this measures relevant with the result of high blood insulin pincers according to the show.People such as Hansen (2007) have measured measuring of insulin sensitivity from OGTT empirically, and this measures relevant with the SI that measures by IVGTT.People such as Mari (2001) have also been developed a kind of measure (OGIS) of insulin sensitivity, this is measured and is based on the dynamic (dynamical) differential equation of glucose that match is described in single time point, determines the amount of several the unknowns so that mate the result of high blood insulin pincers then empirically.Although the OGIS method is based on model at first, by at the single time point match differential equation, many information of glucose and insulin overview (profile) have been left in the basket.

Summary of the invention

A kind of method based on model from oral glucose tolerance test and mixed diet test (mixedmeal) mensuration insulin sensitivity and glucose absorption has been contained in the present invention.The present invention has some advantages than current approach.About four to six blood samples that present technique need obtain during behind the glucose uptake about two to three hours, and thereby be applicable to extensive clinical trial.This analysis relates to the classical least model of simplifying version, only with the method for two parametric description glucose absorption and make that this parameter can be with the integration method of simple algebra acquisition.This method can be differentiated the difference of insulin sensitivity in different patient's types and the improvement of the insulin sensitivity that pharmacotherapy causes reliably.In addition, the insulin sensitivity that obtains with the present invention measures results relevance height (r with high blood insulin pincers ²＞0.8).Thereby this method is a kind of feasible and reliable method of measuring the insulin sensitivity under the physiological condition.

A kind of method from glucose tolerance test or mixed diet test determination insulin sensitivity has been contained in the present invention, and this method needs measurement of glucose levels and analyzes the measurement result that obtains with following formula:

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{{R_a}^{\mathrm{exo}}\left(t\right)}{V_G}-S_I(G\&CenterDot;I_i-G_{\mathrm{basal}}\&CenterDot;I_{\mathrm{basal}})---\left(1\right)$

$\frac{{\mathrm{dI}}_i}{\mathrm{dt}}=\frac{1}{\mathrm{\&tau;}}(I_{\mathrm{plasma}}-I_i)---\left(2\right)$

Wherein

● G (t) is a plasma glucose concentration, and unit is mg/dl

● R _a ^Exo(t) be that the external source glucose appears at the speed (from meals or injection/infusion) in the blood plasma, unit is mg/min

● V _GBe the distribution volume of glucose, unit is dl

● S _IBe insulin sensitivity, unit is 1/min/ (μ U/ml)

● I _i(t) be a matter insulin concentration, unit is that (free the delay, a matter concentration also is lower than plasma concentration to μ U/ml, even under limit between a blood plasma and a matter insulin concentration; In these equations, do not consider this difference.Thereby, to I _i(t) correct understanding should be the ratio that the matter insulin concentration multiply by matter insulin between basic plasma insulin/basis between reality when time t)

● G _BasalBe basic plasma glucose concentration, unit is mg/dl

● I _BasalBe basic plasma insulin concentration, unit is μ U/ml

● τ is transferred to the relevant time constant of interstitial fluid with insulin from blood plasma, and unit is min

● I _PlasmaBe plasma insulin concentration, unit is μ U/ml.

Can obtain the result from the sample of any amount, preferably obtain at least about four to six duplicate samples.The result who obtains from four duplicate samples is enough to measure insulin sensitivity.Cycle obtains the result at any time, and the preferred time cycle is about two to four hours.The result who obtains from two hours time cycles is enough to measure insulin sensitivity.

This method can be used for measuring the effect of therapy to insulin sensitivity.Therapy can be an any means known in the art, includes, but is not limited to pharmacotherapy, trophotherapy or the behavior therapy.

This method has many application, and for example, it can be used for preclinical study to measure the effect of therapy; As the risk of prognosis with the disease of assess patient development such as diabetes or metabolism syndrome; Be used to monitor and/or adjust patient's treatment; Or send with automatic insulin and to be used in combination.

Description of drawings

Fig. 1: wherein two groups plasma glucose and insulin in rosiglitazone (Rosiglitazone) research.The glucose before handling and the meansigma methods of insulin (± s.e.m.) shown in A and the B.8 diabetic subjects of handling with rosiglitazone to the response handled shown in C and the D.

Fig. 2: use S _IAR _aThe S that the A method obtains from OGTT _IAnd the dependency between the GIR during the high blood insulin pincers.The result of A:0.5mU/kg/min infusion of insulin.The result of B:1.5mU/kg/min infusion of insulin.Each point is for to each the value among 18 experimenters in should studying.

Fig. 3: S _IAR _aThe S that the A method obtains _IValue is to the sensitivity about the hypothesis of glucose absorption.11 data points are used for this analysis altogether.A: with the result of the present invention's acquisition.B: with the result of classical least model acquisition.Every line drawing is stated among 18 experimenters wherein one result.Different hypothesis has been described in this article.

Fig. 4: two kinds of different representative overviews that absorb hypothesis.A: constant absorption hypothesis.B: decrescence absorb hypothesis.These two kinds of situations all adopt T _End=210min draws.

The specific embodiment

Insulin resistance plays a major role in several metabolic diseases (comprising diabetes, obesity and hypertension).Reaven(1988)。Therefore, mensuration patient's insulin sensitivity usually causes considerable concern clinically.Two kinds of methods the most received that are used to measure insulin sensitivity are euglycemia-hyperglycemia tongs technology people (1979) such as () DeFronzo and the multisample intravenous glucose tolerance test (FSIVGTT) of using least model to analyze.Bergman(1989)。These two kinds of methods are all sent glucose in unphysiological mode, and thereby provide evaluation to the insulin sensitivity under the artificial condition.In addition, clamp method difficulty in test is big and cost is big, and FSIVGTT needs blood sample collection and modeling analysis continually.Therefore, the means of the insulin sensitivity under the simpler mensuration physiological condition of exploitation are quite attractive.

Developed a blood sample during the simplest method that is used to measure insulin sensitivity is only used condition on an empty stomach.Most popular two kinds is HOMA-IR ((people (1985) such as Matthews) and QUICKI (people (2000) such as Katz), these two kinds of combinations that index is fasting glucose and insulin concentration in these indexes.Although these indexes are easy to obtain, some reports show, it is not fine that other of they and insulin sensitivity are measured dependency.People such as Emoto (1999); People such as Brun (2000); People such as Yokoyama (2003); With people (2003) such as Cutfield.

The invention provides a kind of new being used for from the method based on model of OGTT or mixed diet test determination insulin sensitivity.This method comprise reduced form classical least model, simplyr determine the method for parameter and make glucose absorption speed (R based on integral equation _a) can be only with some hypothesis of two parametric descriptions.This method has some advantages in before this method.At first, can be used on obtain in cycle of two hours few and carry out this method to about four to six parts of blood samples.Secondly, this model only contains three parameters, and these three parameters can be determined from following data: insulin sensitivity (S _I) and describe two parameters of glucose absorption overview.The 3rd, the invention enables parameter value to obtain and to have guaranteed unique solution with simple algebra.At last, compare with classical least model, the result that this simplification mathematical model obtains is lower to the sensitivity about the hypothesis of glucose absorption, and the statistics criterion shows that this simplified model is better than classical least model in these are used.The result who obtains with this method shows that this method can be used for differentiating the difference of the insulin sensitivity in different patient's types, can measure the change of insulin sensitivity response medicine therapy, and the S that measures by this method _IWith the insulin sensitivity dependency height that records by high blood insulin pincers.We are called S with this method _IAR _aA, representative: S _IAnd R _aViaAlgebra.

Provide the following examples to illustrate the present invention rather than restriction the present invention.All lists of references of by this this paper being quoted are incorporated this paper by reference into.

Embodiment

Embodiment 1

Research design and method

S _IAR _aThe A method relates to the simplification version of the classical least model of using glucose metabolism, only with the method for glucose absorption speed and the integration method that finds the optimized parameter value during the feed of two parametric descriptions.The brief overview of these three ingredients is provided below; Subsequently details is described.

Mathematical model

Below mathematical model (having carried out more detailed description below) be used to describe glucose kinetics during the OGTT.

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{{R_a}^{\mathrm{exo}}\left(t\right)}{V_G}-S_I(G\&CenterDot;I_i-G_{\mathrm{basal}}\&CenterDot;I_{\mathrm{basal}})---\left(1\right)$

$\frac{{\mathrm{dI}}_i}{\mathrm{dt}}=\frac{1}{\mathrm{\&tau;}}(I_{\mathrm{plasma}}-I_i)---\left(2\right)$

Wherein

● G (t) is a plasma glucose concentration, and unit is mg/dl

● R _a ^Exo(t) be that the external source glucose appears at the speed (from meals or injection/infusion) in the blood plasma, unit is mg/min

● V _GBe the distribution volume of glucose, unit is dl

● S _IBe insulin sensitivity, unit is 1/min/ (μ U/ml)

● I _i(t) be a matter insulin concentration, unit is that (free the delay, a matter concentration also is lower than plasma concentration to μ U/ml, even under limit between a blood plasma and a matter insulin concentration.In these equations, do not consider this difference.Thereby, to I _i(t) correct understanding should be the ratio that the matter insulin concentration multiply by matter insulin between basic plasma insulin/basis between reality when time t)

● G _BasalBe basic plasma glucose concentration, unit is mg/dl

● I _BasalBe basic plasma insulin concentration, unit is μ U/ml

● τ is transferred to the relevant time constant of interstitial fluid with insulin from blood plasma, and unit is min

● I _PlasmaBe plasma insulin concentration, unit is μ U/ml

Use the appearance speed of two parametric descriptions from the glucose of meals

To studies show that of gastric emptying and glucose absorption, the speed that GLPP occurs is wherein a kind of according in two kinds of overviews generally.People (2005) such as Dalla Man; People such as Hunt (1985); People such as Brener (1983); With people (1996) such as Schirra.In a kind of overview, glucose is absorbed with quite constant speed during after the meal.In another kind of overview, glucose absorption is index and reduces.Describe below and only use two parameter: f ₃₀(ratio of the glucose of the digestion that is absorbed in 30 minutes in beginning) and T _End(time when the most of glucose in the meals has been absorbed) describes each the method in these overviews.

Determine the integration method of parameter value

Can carry out integration to obtain I to equation 2 from measured plasma insulin value _i(t).In each interval of therein glucose and insulin being measured equation 1 is carried out integration then, to obtain the linear algebraic equation of one group of following optimized parameter value:

$\left(\begin{array}{c}G\left(t_2\right)-G\left(t_1\right)\\ G\left(t_3\right)-G\left(t_2\right)+0.9a_{23}\\ G\left(t_4\right)-G\left(t_3\right)+0.9a_{34}\\ .\\ .\\ .\end{array}\right)=\left(\begin{array}{cc}{-\mathrm{\&Phi;}}_{12}& G_{\mathrm{meal}}/V_G\\ {-\mathrm{\&Phi;}}_{23}& a_{23}\\ {-\mathrm{\&Phi;}}_{34}& a_{34}\\ .& .\\ .& .\\ .& .\end{array}\right)\left(\begin{array}{c}{S}_I\\ f_{30}\end{array}\right)---\left(3\right)$

Wherein

● t ₁, t ₂... be the time when measuring glucose and insulin

● G (t _i) be at time t _iThe time plasma glucose

● Φ _IjBe from t _iAnd t _jThe time glucose that records and insulin calculate the integration of gained

● G _MealBe the amount of the glucose of absorption, unit is mg

● a _IjBe the t that calculates gained according to meals deal size and the absorption overview of being supposed _iAnd t _jBetween the measuring of glucose absorption.

Utilize the standard algebra method can obtain to make the S of the variance minimum in the equation 3 easily _IAnd f ₃₀Unique value.Final step is to carry out one dimension optimization to make the best T of match between model and the data to find _EndValue.

Statistical analysis

The result is expressed as meansigma methods ± s.e.m. and checks the comparison of carrying out between the group with t-.Revise red pond quantity of information criterion (Akaike ' s information criteria corrected, AICc) be used to comparison model.People such as Burnham (2002).

Data

Data from two clinical trials carrying out before this are used to verify this method.

Research 1: rosiglitazone research

27 experimenters (15 health suffer from type 2 diabetes mellitus for 12) in this research, have been recruited, to attempt to differentiate the insulin sensitivity labelling.During the placebo introduction period in two weeks (run-inperiod), diabetics is given up any oral drugs, and gets rid of and used the patient of thiazolidinediones medicine or the patient of insulin dependency recently.After this introduction period, 13 experimenters (9 health suffer from diabetes for 4) accept 6 weeks of placebo, and other 14 experimenters (6 health suffer from diabetes for 8) accept rosiglitazone (4mg, twice of every day).The foot couple experimenter carries out OGTT in this introduction period, and carries out once more after handling for 6 weeks.Measure glucose and insulin t=0,30,60,90 and 120 minutes.Measure glucose with method of cracking (Hitachi 747), and measure insulin by RIA (Medigenix Diagnostics).The feature of experimenter before processing is shown in the table 1, and glucose during OGTT and insulin overview are shown in Figure 1.

Table 1: experimenter's baseline characteristic in the test (meansigma methods and (scope))

Research 2:OGTT and the research of high blood insulin pincers

Before in office where the managing, 18 type 2 diabetes mellitus patients that recruit in the clinical trial accept OGTT and comprise the hyperinsulinemic euglycemic clamping test of three steps.Patient's baseline characteristic is shown in the table 1.Preceding two hours of the test of this blood glucose pincers is the introduction period, this introduction period with the 0.25mU/kg/min infusion of insulin.Ensuing two hours (blood glucose pincers test 1), with the 0.5mU/kg/min infusion of insulin, and in the end two hours (blood glucose pincers test 2), with the 1.5mU/kg/min infusion of insulin.During blood glucose pincers test 1 and 2, calculate average glucose infusion rate (GIR) conduct the measuring during last 30 minutes to insulin sensitivity.During OGTT, the t=0 behind glucose uptake, 5,10,15,30,60,90,120,150,180 and 240 molecules are measured glucose and insulin.Measure with method of cracking (Super GAmbulance), and measure insulin by RIA (IKFE).

The result

Research 1

The match of simplified model and data

For 54 kinds of situations of test, the r of match in the equation 3 ²Meansigma methods is 0.96, and the model that hint proposes provides fabulous being similar to of real data.

S in different patient's types _I Difference

Before processing, calculated S to every in 15 non-diabetic experimenters and 12 diabetic subjects _IInsulin sensitivity among the non-diabetic experimenter is significantly higher than diabetic subjects (S _I=10.1 ± 1.3 pairs 4.9 ± 0.7 (10 ^-4/ min/ (μ U/ml)), p＜0.001).

Handle back S _I Increase

Analyze and show S in 14 experimenters that handle with rosiglitazone _ISignificantly increase (the S after the processing _IBefore=14.2 ± 2.4 pairs of processing 6.9 ± 1.3 (10 ^-4/ min/ (μ U/ml), p﹠amp; 1t; 0.05), and S among 13 experimenters in the placebo group _IThere is not (the S in the 6th week of increasing _I=8.1 ± 1.3 pairs the 0th weeks 8.6 ± 1.4).Handle back S with rosiglitazone _IAlmost double similar to the report of the high blood insulin pincers test of using rosiglitazone.People such as Carey (2002); With people (2002) such as Mayerson.

S during repeated measure _I Fluctuation

In the placebo group 13 individual accepts twice OGTT, is separated by for six weeks for twice.For these individualities, the S that is calculated between the measurement _IThe average fluctuation of value is 35 ± 7%.

The glucose absorption parameter

Pass through S _IAR _aThe amount of the glucose that the beginning that the A method is estimated absorbed in 30 minutes will be higher than (f in the non-diabetic experimenter in diabetic subjects ₃₀=0.17 ± 0.01 pair 0.12 ± 0.01, p﹠amp; Lt; 0.01).T in the diabetic subjects _EndShow the trend that accelerates, but this difference not remarkable (T in the diabetic subjects on statistics _End=187 ± 11min is to 211 ± 15min among the non-diabetic experimenter, p=0.2).Rosiglitazone is handled and is not caused f ₃₀Or T _EndIn any marked difference is arranged.For 43 kinds in 54 kinds of situations being tested, adopt constant glucose absorption overview to obtain best fit with data.

Research 2

The result who uses whole 11 duplicate samples to obtain

For among 18 experimenters each, use S _IAR _aThe A method is measured S from OGTT _I, and clamp the GIR that tests during 2 with test 1 of blood glucose pincers and blood glucose and compare.This two kinds of blood glucose pincers test has all been obtained fabulous dependency, as shown in Figure 2.As what expect, because S _IAR _aThe result of A method obtains with OGTT data (wherein insulin concentration remain on physiological range in), thus with the result's of blood glucose pincers test 1 dependency than with the result's of blood glucose pincers test 2 dependency height.

Use only 5 parts of results that blood sample obtains

The effectiveness of this analysis when reducing the blood sample number in order to check only adopts five parts of blood samples of extraction during two hours (t=0,30,60,90 with 120min) to carry out identical analysis.Only use 5 data that obtain during 2 hours with using 4 hours during extract whole 11 somes the time, the S that derives from model _IWith from the dependency between the result of blood glucose pincers (table 2) much at one.The difference that insulin sensitivity has been shown in the table 2 is measured the dependency of the insulin sensitivity of deriving with the test of high blood insulin pincers.With S _IAR _aThe result of A method with can only be used in t=0,30,60,90 and the result of the additive method that carries out of 5 data points of gathering during 120min advanced relatively.

Table 2

The insulin sensitivity method	GIR during the blood glucose pincers test 1	GIR during the blood glucose pincers test 2
			??S IAR aA (using 11 samples)	??r 2＝0.82	??r 2＝0.65
??S IAR aA (using 5 samples)	??r 2＝0.85	??r 2＝0.59
			??HOMA-IR?(4)	??r 2＝0.40	??r 2＝0.37
??QUICKI??(5)	??r 2＝0.57	??r 2＝0.39
			??ISI cst??(13)	??r 2＝0.60	??r 2＝0.43
??ISI comp(14)	??r 2＝0.70	??r 2＝0.49
			??BIGTT-S I10-30-120(15)	??r 2＝0.78	??r 2＝0.56
??BIGTT-S I10-60-120(15)	??r 2＝0.75	??r 2＝0.49
			??OGIS??(16)	??r 2＝0.55	??r 2＝0.47

Compare with the result of other insulin sensitivity methods

5 of during behind the OGTT 2 hours, gathering of use or still less the data point insulin sensitivity that also can easily calculate several previous propositions measure.Calculate the insulin sensitivity value that obtains with these methods and itself and high blood insulin clamped the result relevant.S _IAR _aThe result of A method is than the result and the blood glucose pincers result's of any additive method dependency higher (table 2).

The result is to the comparison of sensitivity and the simplified model and the classical least model of modeling assumption

As described below, can analyze with the simplified model that the alternative this paper of classical least model proposes.When using classical least model, also need determine an additional parameter SG of glucose-sensitive.

The details of mathematical model

The description of model

Circulating glucose concentration can be described by following equation:

$V_G\frac{\mathrm{dG}}{\mathrm{dt}}={R_a}^{\mathrm{exo}}\left(t\right)+{R_a}^{\mathrm{end}}(G,I_i)-R_d(G,I_i)---\left(A1\right)$

V wherein _GBe the distribution volume (dl) of glucose, G is plasma glucose concentration (mg/dl), I _iBe a matter insulin concentration (μ U/ml), R _a ^ExoAnd R _a ^EndBe respectively appearance speed (unit is mg/min) from the glucose in external source (as meals or infusion) and inner source (liver, kidney), and R _dBe glucose metabolism clearance rate (unit is mg/min), t is time (unit is min).

R _a ^End(G, I _i)-R _d(G, I _i) the item nonlinear function of glucose and insulin normally, it is not for known fully.But we know, the basis, when spending the night on an empty stomach state, R _a ^End(G _Basal, I _Basal)-R _d(G _Basal, I _Basal)=0.In addition, we know that also the two all plays glucose and insulin the effect that reduces the output of endogenous endogenous glucose and play the effect that increases the glucose metabolism removing.Therefore, following being similar to proposed

R _a ^end(G，I _i)-R _d(G，I _i)≈-S _I(G·I _i-G _basal·I _basal)(A2)

Should approximate only use single parameter to satisfy two kinds of above-mentioned situations, this single parameter be S _I, its unit is 1/min/ (μ U/ml).Equation (A2) substitution equation (A1) is obtained the equation 1 of text.In addition, the equation 2 of text is used to illustrate with insulin between blood plasma and interstitial fluid, shifts relevant time delay.

Comparison with classical least model

Classical least model (Bergman (1989)) is

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{{R_a}^{\mathrm{exo}}\left(t\right)}{V_G}-\mathrm{XG}-p_1(G-G_{\mathrm{basal}})---\left(A3\right)$

$\frac{\mathrm{dX}}{\mathrm{dt}}={-p}_{2}X+p_3(I_{\mathrm{plasma}}-I_{\mathrm{basal}})---\left(A4\right)$

By definition I _i=(p ₂/ p ₃) X+I _Basal, S _I=p ₃/ p ₂And S _G=p ₁, τ=1/p ₂, equation A4 is suitable with equation 2, and equation A3 becomes

Notice that equation A5 is suitable with equation 1, more than the classical least model (S additionally _G-S _II _Basal) (G-G _Basal).Difference item S _G-S _II _BasalBe called GEZI (the glucose utilization usefulness when zero insulin) and it is reported and be difficult to accurately estimate GEZI, especially when the sample number that extracts is limited from the IVGTT data.People such as Sakamoto (1997).S when using classical least model _IAR _aThe A method also is (as described below) that is suitable for, but when analyzing the OGTT data, the simplified model that uses equation 1-2 to describe has obtained better result.

The speed of using two parametric descriptions to occur from meals

The result who determines the gastric emptying study of glucose absorption speed and tracer study usually shows wherein a kind of in two kinds of different overviews of gastric emptying and/or glucose absorption.In a kind of therein overview, exist the quick stage of initial gastric emptying, follow by the adjusting stage, about 2-4kcal/min is by gastric emptying in the adjusting stage.People such as Hunt (1985); With people (1983) such as Brener.Glucose absorption speed also increases fast, reaches stationary value then until the quick decay when meals almost completely are absorbed.In another kind of overview, the speed of gastric emptying and glucose absorption all increases fast, continues to reduce to seem the mode that is exponential then.People such as Schirra (1996).The example of these two kinds of overviews all can find in people (2005a) such as () Dalla Man, the similar constant overview described herein of OGTT wherein, and the similar decrescence overview of mixed diet test.Different overviews may be (as solid to liquid) and/or individual variability because the food type that consumed.Owing to know that in advance which kind of overview do not bring out the most suitable given patient/meals, so two kinds of overviews are all done approximate and obtained a kind of overview of best fit with Model Selection.

Although similar above-mentioned those gastric emptying overview usually has report, the individuality that also exists gastric emptying significantly to be delayed.This comprises the patient who suffers from gastroparesis, and may occur carrying out some treatment (for example use Yi Kena peptide (exenatide) treatment) time.Thereby this analysis does not suppose that when gastric emptying is initial be fast; But, model is used for determining glucose absorbed ratio (parameter f in 30 minutes of beginning of meals ₃₀).Do like this and make and with this model except being used to differentiate that insulin sensitivity changes, can also be used to differentiate the change of gastric emptying and/or alimentation.

Next, several hypothesis make to calculate and relate to as f ₃₀The R of function _a ^EndAll integrations.At first, suppose the end of term after the meal, 90% glucose of being taken in is absorbed.People (2004) such as Dalla Man have also used this value, and this value is in the scope (70-100%) of bibliographical information value.People such as Caumo (2000); With people (1998) such as Livesey.Time representation when the meals with 90% have been absorbed is T _EndAnd this parameter can obtain by solving the one dimension optimization problem, as described later.

For amount at the follow-up systemic glucose of interval, come above-mentioned glucose absorption overview is done approximate by doing following hypothesis, this is shown in Figure 4.

Constant absorption hypothesis hypothesis is at t=30 and t=T _EndBetween the absorption of glucose be constant and suppose t=T _EndThe time, 90% glucose of being taken in is absorbed.Thereby, at t=30 and t=T _EndBetween, R _a ^Exo(t)=G _Meal(0.9-f ₃₀)/(T _End-30), G wherein _MealBe the amount of glucose in the meals, unit is mg.

Decrescence absorb hypothesis and suppose t=30 and t=T here _EndBetween glucose absorption speed linearly descend, and at t=T _EndThe time be 0.For for simplicity, the overview rather than be index decreased of having selected linearly to descend.Thereby, at t=30 and t=T _EndBetween, R _a ^Exo(t)=2G _Meal(0.9-f ₃₀) (T _End-t)/(T _End-30) ²

Use integration method to determine parameter value

The method of integration least model equation has been used to adopt during the critical care of continuous glucose monitoring is provided with before this, and wherein speed to occur be known to glucose.People such as Hann (2005); With people (2006) such as Chase.Here, glucose occurs having developed a kind of similar method in the situation of speed the unknown therein.In the derivation of back, initial two time points when supposing to measure are t=0 and t=30 minute, but this can easily make amendment.

Allow t ₁, t ₂..., t _nFor the time point of measuring glucose and insulin (wherein, as mentioned above, has used t ₁=0 and t ₂=30 are used to illustrate).Then, at two time point t _jAnd t _kBetween integration carried out on the both sides of equation 1 obtain

$G\left(t_k\right)-G\left(t_j\right)=\frac{1}{V_G}\underset{t_j}{\overset{t_k}{\&Integral;}}{R_a}^{\mathrm{exo}}\left(t\right)\mathrm{dt}-S_I\underset{t_j}{\overset{t_k}{\&Integral;}}(G\left(t\right)\&CenterDot;I_i\left(t\right)-G_{\mathrm{basal}}\&CenterDot;I_{\mathrm{basal}})\mathrm{dt}---\left(A6\right)$

For above-mentioned two kinds of absorption overviews, can easily carry out integration and obtain first integral equation A6.In both cases

$\underset{0}{\overset{30}{\&Integral;}}{R_a}^{\mathrm{exo}}\left(t\right)\mathrm{dt}={\mathrm{<figure-callout\; id="30"\; label="f"\; filenames="A2008800128180029H1.png"\; state="\{\{state\}\}">f</figure-callout>}}_{30}\&CenterDot;G_{\mathrm{meal}}---\left(A7\right)$

Pass through f ₃₀Definition obtain.For other times at interval,

$\underset{t_j}{\overset{t_k}{\&Integral;}}{R_a}^{\mathrm{exo}}\left(t\right)\mathrm{dt}=w_{\mathrm{jk}}(0.9-f_{30})\&CenterDot;G_{\mathrm{meal}}---\left(A8\right)$

Wherein

w _Jk=(t _k-t _j)/(T _End-30) be used for the constant absorption hypothesis

w _Jk=((T _End-t _j) ²-(T _End-t _k) ²)/(T _End-30) ²Be used for decrescence absorbing hypothesis

For the second integral among the accounting equation A6, at first based on the I of measured plasma insulin concentration analytic equation 2 _i(t).For this reason, by at measured time point (promptly for t _j＜t＜t _k) between do linear interpolation and define I _Plasma(t).

$I_{\mathrm{plasma}}\left(t\right)=I_{\mathrm{plasma}}\left(t_j\right)+\frac{I_{\mathrm{plasma}}\left(t_k\right)-I_{\mathrm{plasma}}\left(t_j\right)}{t_k-t_j}(t-t_j)$

Then, can be at each interval (t wherein _j≤ t≤t _k) analytic equation 2, obtain

$I_i\left(t\right)={\mathrm{\&alpha;}}_{\mathrm{jk}}+{\mathrm{\&beta;}}_{\mathrm{jk}}{e}^{-\left({t-t}_j\right)/\mathrm{\&tau;}}+m_{I_{\mathrm{jk}}}(t-t_j)---\left(A9\right)$

Wherein

$m_{I_{\mathrm{jk}}}=(I_{\mathrm{plasma}}\left(t_k\right)-I_{\mathrm{plasma}}\left(t_j\right))/(t_k-t_j)$

δI _j＝I _i(t _j)-I _plasma(t _j)

${\mathrm{\&alpha;}}_{\mathrm{jk}}=I_{\mathrm{plasma}}\left(t_j\right)-\mathrm{\&tau;}\&CenterDot;m_{I_{\mathrm{jk}}}$

${\mathrm{\&beta;}}_{\mathrm{jk}}={\mathrm{\&delta;I}}_j+\mathrm{\&tau;}\&CenterDot;m_{I_{\mathrm{jk}}}$

In order to obtain at interval t with equation 9 _j≤ t≤t _kInterior I _i(t), I _i(t _j) must be known.By setting I _i(0)=I _Plasma(0)=I _Basal, this can be at first interval (t wherein ₁=0 and t ₂=30) realize in.In the later time interval, I _i(t _j) can be at interval t before this _i≤ t≤t _jIn obtain from equation A9.

Now, the I by substitution equation A9 _i(t) and between measured data point, do linear interpolation (as doing), about insulin but the second integral among the accounting equation A6.So obtain

${\mathrm{\&Phi;}}_{\mathrm{jk}}=\underset{t_j}{\overset{t_k}{\&Integral;}}(G\left(t\right)I_i\left(t\right)-G_{\mathrm{basal}}{I}_{\mathrm{basal}})\mathrm{dt}={\mathrm{\&delta;t}}_{\mathrm{jk}}({\mathrm{\&alpha;}}_{\mathrm{jk}}G\left(t_j\right)-G_{\mathrm{basal}}{I}_{\mathrm{basal}})+({\mathrm{\&alpha;}}_{\mathrm{jk}}{m}_{G_{\mathrm{jk}}}+m_{I_{\mathrm{jk}}}G\left(t_j\right))\frac{{\left({\mathrm{\&delta;t}}_{\mathrm{jk}}\right)}^2}{2}$

$+m_{I_{\mathrm{jk}}}{m}_{G_{\mathrm{jk}}}\frac{{\left({\mathrm{\&delta;t}}_{\mathrm{jk}}\right)}^3}{3}+{\mathrm{\&tau;\&beta;}}_{\mathrm{jk}}G\left(t_j\right)(1-e^{-\mathrm{\&delta;}{t}_{\mathrm{jk}}/\mathrm{\&tau;}})+{\mathrm{\&tau;}}^2{\mathrm{\&beta;}}_{\mathrm{jk}}{m}_{G_{\mathrm{jk}}}(1-e^{-{\mathrm{\&delta;t}}_{\mathrm{jk}}/\mathrm{\&tau;}}(1+\frac{{\mathrm{\&delta;t}}_{\mathrm{jk}}}{\mathrm{\&tau;}}))---\left(A10\right)$

Wherein

And δ t _Jk=t _k-t _j

By in each interval, using equation A6, use the result shown in the equation A7-A10, and definition a _Jk=-w _JkG _Meal/ V _G, can obtain the equation 3 in the text.When existing in the situation of the extra measurement of carrying out between t=0 and the t=30 therein, still use equation 3, and Φ ₁₂By the integration in the subinterval between 0 and 30 being added and calculating.

Make the S of the variance minimum in the equation 3 _IAnd f ₃₀Value by following formula (referring to, for example, (Mirsky (1972))) provide:

$\left(\begin{array}{c}{\mathrm{<figure-callout\; id="30"\; label="S\; I\; f"\; filenames="A2008800128180029H1.png"\; state="\{\{state\}\}">S</figure-callout>}}_I& \\ f_{}{}_{30}\end{array}\right)={\left(A^{T}A\right)}^{-1}{A}^{T}b$

Wherein

$A=\left(\begin{array}{cc}-{\mathrm{\&Phi;}}_{12}& G_{\mathrm{meal}}\\ {-\mathrm{\&Phi;}}_{23}& a_{23}\\ {-\mathrm{\&Phi;}}_{34}& a_{34}\\ .& .\\ .& .\\ .& .\end{array}\right),b=\left(\begin{array}{c}G\left(t_2\right)-G\left(t_1\right)\\ G\left(t_3\right)-G\left(t_2\right)+0.9a_{23}\\ G\left(t_4\right)-G\left(t_3\right)+{0.9a}_{34}\\ .\\ .\\ .\end{array}\right)$

And ^TWith ^-1Difference representing matrix transposition and matrix inversion.

Use least model

Can use classical least model to use this same procedure.In this case, the equation in the text 3 is replaced by:

$\left(\begin{array}{c}G\left(t_2\right)-G\left(t_1\right)\\ G\left(t_3\right)-G\left(t_2\right)+{0.9a}_{23}\\ G\left(t_4\right)-G\left(t_3\right)+{0.9a}_{34}\\ .\\ .\\ .\end{array}\right..=\left(\begin{array}{ccc}{-\mathrm{\&Phi;}}_{12}& {-\mathrm{\&Theta;}}_{12}& G_{\mathrm{meal}}\\ -\mathrm{\&Phi;}& 23{-\mathrm{\&Theta;}}_{23}& a_{23}\\ {-\mathrm{\&Phi;}}_{34}& -{\mathrm{\&Theta;}}_{34}& a_{34}\\ .& .& .\\ .& .& \text{.}\\ .& .& \text{.}\end{array}\right)\left(\begin{array}{c}{S}_I\\ \mathrm{GEZI}\\ f_{30}\end{array}\right)---\left(A11\right)$

Wherein To calculate with the similar method of above-mentioned integration.

The parameter value that is used for embodiment

1. in all analyses of carrying out, adopted V _G=1.5dl/kg, τ=60.In rudimentary check, checked some different τZhi, τ=60 provide the best overall match to data.V _GConsistent with report in other researchs, and τZhi is similar to the 1/p in the classical least model of having reported ₂Intermediate value.People (2004) such as Dalla Man.

T _EndValue is optimized algorithm available from the one dimension of standard.For T _EndEach value, S is provided _IAnd f ₃₀The least square solution acquisition as discussed previously of optimal value.Be chosen at and obtain best fit between model and test data and (pass through r ²Judgement) T _EndValue.

Function f minbnd is used to solve optimization problem, and this value is limited between 150 to 270min.

Parameter estimation is to absorbing the sensitivity of hypothesis

This analyzes hypothesis, and the glucose absorption overview can be done approximate by a kind of in two kinds of forms shown in Figure 3.Because the two all is approximate to real overview, is important so assessment result has many sensitivities to the hypothesis that absorbs overview.In previous analysis, the absorption overview that provides the data best fit is provided is used for every experimenter.Here, for following three kinds of different hypothesis to the glucose absorption overview, the result is compared: (1) " constant ": used the constant absorption overview, (2) " decrescence ": used straight line to reduce and absorbed overview and (3) " best fit ": adopted that obtains best fit in these two kinds of overviews.Use contains the whole data set of 11 parts of blood samples and the reduction data of being made up of 5 parts of blood samples gathering in two hours.In addition, in order to compare between the simplified model that proposes at this paper and the classical least model, also adopt this parameter determination method to carry out this analysis with classical least model.The result who uses simplified model to obtain is insensitive to absorbing hypothesis, and the result who uses classical least model to obtain is more responsive to these hypothesis, shown in table 3 and Fig. 3.When using classical least model, minus S _IValue obtains best fit (relatively large S once in a while _GWith minus S _IThe match that can obtain sometimes).When using simplified model, absorb the S that hypothesis is obtained with difference _IThe average variation of value is less than 5%, when using classical least model then greater than 150%.S has been shown in the table 3 _I(10 ^-4Meansigma methods/min/ (μ U/ml)) (± s.e.m.).For every experimenter, to calculate S as the described 6 kinds of different modes of text _IThe result of simplified model is than more insensitive to absorbing hypothesis with the result that classical least model obtained.In addition, simplified model obtains a good result when only using 5 data points, and classical least model can not obtain a good result.

Table 3

Red pond quantity of information criterion thinks that simplified model is better than classical least model

Red pond quantity of information criterion (AIC) is based on (Akaike (1974)) of information theory development, and this criterion is the excellent benign statistics balancing method that is used for the assessment models fitting data that often uses.This criterion seeks to determine the good property of model match test data and the optimum balance between the model complexity.Owing to have only fewer purpose measured value, so adopted AICc.People such as Schirra (1996).

AICc thinks that for OGTT, the simplified model of glucose metabolism should be better than classical least model, especially when gathering fewer strong point.When only using 5 data points, this simplified model is preferred all experimenters in two kinds of researchs.In research 2, this simplified model is preferred in surpassing 90% experimenter when using 6 data points (t=0,30,60,90,120 and 180), and this simplified model is preferred in surpassing 70% experimenter when using 11 data points.

Discuss

It is quite attractive that acquisition is used to be determined at the reliable and suitable method of the insulin sensitivity under the physiological condition.This method aspect test and the analysis aspect all very convenient, and thereby can be used for extensive clinical trial.Therefore, this method can adopt OGTT or mixed diet test, uses few extremely about 5 blood samples of gathering during about 2 hours to carry out.All correct among the experimenter that the hypothesis relevant with this method handled in undressed experimenter and with multiple pharmacotherapy (comprise and change insulin secretion, insulin sensitivity and/or glucose absorption speed).In addition, the results relevance height of the result of this method generation and the research of high blood insulin pincers.At last, adopt this method for convenience, the result is easy to acquisition and need not professional software.

Proposed some kinds recent years and be used for from the method for OGTT assessment insulin sensitivity, for example, people (2005a) such as Dalla Man; People (2005b) such as Dalla Man; People such as Caumo (2000); People such as Stumvoll (2000); People such as Matsuda (1999); People such as Hansen (2007); With people (2001) such as Mari.Although these methods make progress, do not have in Fa Zhan the method before this a kind ofly can satisfy above-mentioned standard fully.Empirical approach is to utilize untreated experimenter to derive, and thereby, these relations will keep how good unclearly for various therapy.OGIS method people (2001) such as () Mari has the advantage that only needs 3 parts of blood samples, and makes and can determine insulin sensitivity from algebraic expression.Yet this method has some limitation.At first, every individuality of this method hypothesis has identical glucose absorption speed constantly in the t=90 moment or t=120min.This hypothesis is in-problem in undressed experimenter, and for as change the Acarbose (acarbose) of glucose absorption speed or the processing of Exenatide (exenatide), correct probability even lower.The second, by attempting to describe the dynamic (dynamical) ordinary differential equation of glucose in single time point match, available many information can be left in the basket in the data.At last, though the OGIS method comprise many through specific match to mate the parameter of high blood insulin pincers data, with independently blood glucose pincers correlation of data is very not high yet.Value r ²Even=0.55 is higher than the value (Akaike (1974)) of other data acquisitions of usefulness of being reported, yet this dependency is suitable with the value that obtains with the QUICKI that only needs a blood sample.

Caumo method (2000) supposes that glucose absorption speed plasma glucose curve closely mates.Seem in undressed experimenter rationally though this is similar to, the therapy such as insulin reinforcing agent and/or euglycemic agent can change the blood plasma blood sugar concentration under the situation that does not change glucose absorption speed.Thereby, during response that this hypothesis is crossed in comparison process or undressed, may be incorrect.In addition, the needed measurement of the derivation of equation will be carried out after the sufficiently long time after the meal so that glucose and insulin action are all got back to baseline value, this means that this method needs data collection at least 3 hours behind OGTT.It is reported the result that method that people (2005a) such as Dalla Man proposes obtains getting a good chance of in undressed experimenter, but it needs at least 7 parts of blood samples and this method need determine and the as many parameter of data point of being gathered.In addition, this method needs special modeling software, and the prior distribution of requirements definition parameter to be improving their confirmability, and can not guarantee to find unique optimal solution.The comparison about the hypothesis of glucose absorption of several different methods has been shown in the table 4.

Table 4

Method	Hypothesis about glucose absorption	Absorption parameter from data fitting
			S IAR aA	● suppose the shape of the fine approximate glucose absorption overview of wherein a kind of energy in two kinds of overviews shown in Fig. 4.● behind OGTT, 90% glucose of being taken in appears in the body circulation.	● f 30● T End● the shape (constant or decrescence) of the overview of best fit is provided
People (2007) such as OGIS Hansen	● suppose to have identical glucose absorption speed in the t=90 moment or the t=120min moment every individuality	Do not have
			Caumo (2000)	● suppose " the expection form " of the similar plasma glucose drift of shape of glucose absorption overview.● 80% glucose of being taken in appears in the body circulation behind OGTT.	Do not have
Dalla Man (2005a)	● absorption is described to piecewise linear function; Value at each measurement point is determined from data.● 90% glucose of being taken in appears in the body circulation behind OGTT.	● determine that parameter at each time point of measuring glucose is to obtain R a ExoPiecewise linearity represent

S provided herein _IAR _aThe A method satisfies all standards of practical approach.Except aspect test and the analysis aspect is easy to carry out, verified this method in some kinds of modes.According to the show, this method can be distinguished different patient's types, can only use the minority experimenter to differentiate the change of insulin sensitivity response medicine therapy and S _IAR _aThe results relevance height of the result of A method and high blood insulin pincers.Importantly, the result supposes relative insensitivity to the difference of being done in analysis according to the show.

Although this analysis side overweights from OGTT and measures insulin sensitivity, also can be used for other potential application.Because this method can be determined to begin the amount of the glucose that absorbed in 30 minutes and information about the shape of after this absorption overview is provided, so this method might can be used for the diagnosing diabetes gastroparesis or other relate to the situation of inappropriate gastric emptying.Another potential application is to determine that with being used for parameter the integration method of method is applied to the FSIVGTT data.Though with this S _IAR _aThis simplified model had some advantages when the A method was used for the OGTT data, but classical minimum method might be preferred (the extra glucose utilization effectiveness parameters of classical least model helps to fit within the glucose responding behind the quick intravenous injection glucose) when this method is used for the FSIVGTT data.

Two other field of the future studies of being advised is that further checking is brought out checking this method by the glucose absorption estimated value of this method acquisition and at mixed diet.Determined f ₃₀Value and people (2005a) such as () Dalla Man use the data consistent of tracer report.Because what not having in the derivation of this method is distinctive to OGGT, so expection this method also should be applicable to the mixed diet test.Use from mixed diet test for data check this method and show the fabulous (r of the concordance between this model and the test data ²＞0.95).

The same with any method that mathematical modeling is applied to the analytical test data, in this analysis, done several hypothesis.Here the main hypothesis of being done is: (1) clean after the meal glucose metabolism clearance rate can be passed through S _I(GI-G _BasalI _Basal) carry out rationally being similar to, the shape of the glucose absorption overview after (2) 30 minutes can rationally be similar to by wherein a kind of the carrying out in described 2 kinds of overviews, and (3) the glucose distribution volume with insulin shift time constant that into interstitial fluid is relevant be given rather than from data fitting come the time, can obtain a good result.Fabulous fitness (r between this model and the data ²～0.95) show, suppose that (1) is correct to the present application of checking, and the sensitivity analysis of being carried out and red pond quantity of information criterion shows, in these are used, should approximate be better than classical least model.In addition, this method makes and can test to other models (comprising classical least model) as required.That supposes that (2) provide approximately conforms to the glucose absorption data with gastric emptying; Other overviews also can be by regulation w _IjParameter having deferent value is checked.At last, in order to obtain reliable estimation from a limited number of data point, to V to the concern parameter _GWith τ done the regulation rather than attempt from data fitting they.This method provides the overall fit relevant with parameter value to measure and uncertain estimate, described parameter value can be used for assessment and whether exists that wherein these suppose inappropriate situation.

Put it briefly, this method is measured insulin sensitivity and the glucose absorption during OGTT or the mixed diet.S _IAR _aThe A method by the dynamic (dynamical) simplification mathematical model of glucose, new be used for the method for the glucose absorption during approximate meals or the OGTT and make that parameter can be with the definite integration method of algebraic expression that can carry out at the standard electronic form easily.According to the show, this method can be distinguished different patient's types, differentiate the change of the insulin sensitivity that is caused by pharmacotherapy, and S _IAR _aThe dependency height of the result of A method and high blood insulin pincers.This method provides a kind of convenience and reliable means that are used to be evaluated at the insulin sensitivity under the physiological condition.

List of references

Akaike(1974)A?new?look?at?statistical?model?identification.IEEETransactions?on?Automatic?Control?19：716-723

People such as Allen, (2006) Halofenate is a selective peroxisome proliferator-activated receptor gamma modulator with antidiabetic activity Diabetes55:2523-33

American?Diabetes?Association(1996)Self-monitoring?of?blood?glucoseconsensus?statement?Diabetes?Care?19(Suppl?1)：S62-6

Bergman(1989)Lilly?lecture?1989.Toward?physiological?understandingof?glucose?tolerance.Minimal-model?approach?Diabetes?38：1512-1527

People such as Brener, (1983) Regulation of the gastric emptying of glucoseGastroenterol 85:76-82

People such as Brun, (2000) Homeostasis model assessment and related simplifiedevaluations of insulin sensitivity from fasting in sulin and glucoseDiabetes Care 23:1037-1038

People such as Burkey, (2005) Acute and chronic effects of the incretin enhancervildagliptin in insulin-resistant rats J Pharmacol Exp Ther 315:688-95

People such as Carey, (2002) Effect of Rosiglitazone on insulin sensitivity andbody composition in type 2diabetic patients Obes Res 10:1008-1015

People such as Caumo, (2000) insulin sensitivity from meal tolerance tests innormal subjects:a minimal model index J Clin Endocrinol Metab 85:4396-4402

People such as Chase, (2006) Integral-based filtering of continuous glucosesensor measurements for glycaemic control in critical care Comput MethodsPrograms Biomed 82:238-247

People such as Chiasson, (1996) The effect of acarbose on insulin sensitivity insubjects with impaired glucose tolerance Diabetes Care 19:1190-1193

People such as Cutfield, (2003) Evaluation of HOMA and QUICKI as measures ofinsulin sensitivity in prepubertal children Pediatr Diabetes 4:119-125

People such as Dalla Man, (2004) Minimal model estimation of glucose absorptionand in sulin sensitivity from oral test:validation with a tracer method AmJ Physiol Endocrinol Metab 287:637-643

People such as Dalla Man, (2005a) Two-hour seven sample oral glucose tolerancetest and meal protocol:minimal model assessment of beta-cell responsivityand insulin sensitivity in nondiabetic individuals Diabetes 54:3265-3273

People such as Dalla Man, (2005b) insulin sensititivity by oralg lucose minimalmodels:validation against clamp Am J Physiol Endocrinol Metab 289:954-959

People such as DeFronzo, (1979) Glucose clamp technique:a method for quantifyinginsulin secretion and resistance Am J Physiol 237:E214-223

People such as Delgado, (2002) Acarbose improves indirectly both insul inresistance and secretion in obe se type 2 diabetic patients Diabetes Metab28:195-200

People such as Emoto, (1999) Homeostasis model assessment as a clinical index ofinsulin resistance in type 2 diabetic patients treated with sulfonylureasDiabetes Care 22:818-822

People such as Gastaldelli, (2007) Thiazolidinediones improve β-cell function intype 2 diabetic patients Am J Physiol Endocrinol Metab 292:E871-83

People such as Hann, (2005) Integral-based parameter identification for long-termdynamic verification of a glucose-insulin system model Comput MethodsPrograms Biomed 77:259-270

People such as Hansen, (2007) The BIGTT Test:A novel test for simultaneousmeasurement of pancreatic β-cell function, insulin sensitivity, andglucose tolerance Diabetes Care 30:257-262

People such as Hatanaka, (1994) The measurement of gastric emptying in consciousrats by monitoring serial changes in serum acetaminophen level J PharmacolToxicol Methods 31:161-5

People such as Hsieh, (2007) Both slow-release and regular-form metformin improveglycemic control without altering plasma visfatin level in patients withtype 2 diabetes mellitus Metabolism 56:1087-92

People such as Hunt, (1985) Effect of meal volume and energy density on thegastric emptying of carbohydrates Gastroenterol 89:1326-1330

People such as Katz, (2000) Quantitative insulin sensitivity check index:asimple, accurate method for assessing insulin sensitivity in humans J ClinEndocrinol Metab 85:2402-2410

People such as Livesey, (1998) Simultaneous time-varying systemic appearance oforal and hepatic glucose in adults monitored with stable isotopes Am JPhysiol 275 (4 Pt 1): 717-728

People such as Mari, (2001) A model-based method for assessing insulinsensitivity from the oral glucose tolerance test Diabetes Care 24:539-548

People such as Mari, (2005) Vildagliptin, a Dipeptidyl Peptidase-IV Inhibitor, Improves Model-Assessed β-Cell Function in Patients with Type 2 DiabetesJCEM 90:4888-4894

People such as Matsuda, (1999) insulin sensitivity indices obtained from oralglucose tolerance testing:comparison with the euglycemic insulin clampDiabetes Care 22:1462-1470

People such as Matthews, (1985) Homeostasis model assessment:insulin resistanceand beta-cell function from fasting plasma glucose and insulinconcentrations in man Diabetologia 28:412-419

People such as Mayerson, (2002) The effects of Rosiglitazone on insulinsensitivity, lipolysis, and hepatic and skeletal muscle triglyceridecontent in patients with Type 2 Diabetes Diabetes 51:797-802

People such as Medhus, (2001) Gastric emptying:the validity of the paracetamolabsorption test adjusted for individual pharmacokinetics NeurogastroenterolMot 13:179-85

People such as Meneilly, (2000) Effect of acarbose on insulin sensitivity inelderly patients with diabetes Diabetes Care 23:1162-7

People such as Mokdad, (2003) Prevalence of obesity, diabetes, and obesity-related health risk factors, 2001 JAMA 289:76-79

People such as Natalucci, (2003) Age-related ana lysis of glucose metabolism inspontaneously hypertensive and normotensive rats Exp Physiol 88:399-404

People such as Ovalle, (2004) Effect of rosiglitazone versus insulin on thepancreatic β-cell function of subjects with Type 2 Diabetes Diabetes Care27:2585-2589

People such as Polidori, (2008) S _IAR _aA method for determining insulin sensitivityand glucose absorption Part 2:Application in Animals Highlights DisparateResponse to Therapies

Polidori(2008)S _IAR _aA：A?Simple?Method?for?Determining?insulinsensitivity?and?glucose?absorption?Rates?from?Oral?Glucose?Tol?erance?Tests.Part?1：Validation?in?Humans

People such as Rasouli, (2007) Effects of pioglitazone and metformin on β-cellfunction in nondiabetic subjects at high risk for Type 2 Diabetes Am JPhysiol Endocrinol Metab 292:E359-65

Reaven(1997)Banting?Lecture?1988.Role?of?insulin?resistance?in?humandisease?1988?Nutrition?13：65

People such as Richardson, (2006) Effects of rosiglitazone and metformin onpancreatic beta cell gene expression Diabetologia 49:685-96

People such as Rivers, (2006) Precision and Accuracy of Two Blood Glucose Meters:FreeStyle Flash Versus One Touch Ultra Am J Heal th-Syst Pharm 63:1411-1416

People such as Rose, (2001) Effect of prior exercise on glucose metabolism intrained men Am J Physiol Endocrinol Metab 281:E766-71

People such as Sakamoto, (1997) The accuracy of glucose effectiveness at zeroinsulin with reduced sample protocol from the minimal model Med Sci SportsEx 29:20

People such as Schirra, (1996) Gastric emptying and release of incretin hormonesafter glucose ingestion in humans J Clin Invest 97:92-103

People such as Seltzer, (1967) Insulin secretion in response to glycemicstimulus:relation of delayed initial release to carbohydrate intolerancein mild diabetes mellitus J Clin Invest 46:323-35

People such as Stumvoll, (2000) Use of the oral glucose tolerance test to assessinsulin release and insulin sensitivity Diabetes Care 23:295-301

People such as van Doorn, (2006) Evaluation of proinflammatory cytokines andinflammation markers as biomarkers for the action of thiazolidinediones inType 2 Diabetes mellitus patients and healthy volunteers Br J ClinPharmacol 62:391-402

People such as van Doorn, (2007) Evaluation of metabolite profiles as biomarkersfor the pharmacological effects of thiazolidinediones in Type 2 Diabetesmellitus patients and healthy volunteers Br J Clin Pharmacol 63:562-74

People such as Vella, (2007) Effects of dipeptidyl peptidase-4 inhibition ongastrointestinal function, meal appearance, and glucose metabolism in Type2 Diabetes Diabetes 56:1475-80

People such as Vidon, (1988) Metformin in the digestive tract Diabetes Res ClinPract 4:223-9

People such as Wachters-Hagedoorn, (2006) The rate of inte stinal glucoseabsorption is correlated with plasma glucose-dependent insulinotropicpolypeptide concentrations in healthy men J Nutr 136:1511-6

People such as Weitgasser, (1999) Newer portable glucose meters--analyticalimprovement compared with previous generation devices? Clin Chem 45:1821-5

People such as Yasuda, (2004) Metformin causes reduction of food intake and bodyweight gain and improvement of glucose intolerance in combination withdipeptidyl peptidase IV inhibitor in Zucker fa/fa rats J Pharmacol Exp Ther310:614-9

People such as Yokoyama, (2003) Quantitative insulin sensitivity check index andthe reciprocal index of homeostasis model assessment in normal range weightand moderately obese type 2 diabetic patients Diabetes Care 26:2426-2432

Claims (10)

1. method from oral glucose tolerance test or mixed diet test determination insulin sensitivity said method comprising the steps of:

Measure after the meal blood glucose and insulin level

Analyze described measurement, described analysis is used:

A. the differential equation that illustrates below (1) and (2)

B. with 1-2 parameter at least speed is appearred in the glucose from meals and do proximate method, as shown in Figure 4

C. the integration method described of present patent application, described integration method makes that described parameter can be by the acquisition of the algebraic equation shown in the analytic equation 3

$\frac{\mathrm{dG}}{\mathrm{dt}}=\frac{{R_a}^{\mathrm{exo}}\left(t\right)}{V_G}-S_I(G\&CenterDot;I_i-G_{\mathrm{basal}}\&CenterDot;I_{\mathrm{basal}})---\left(1\right)$

$\frac{{\mathrm{dI}}_i}{\mathrm{dt}}=\frac{1}{\mathrm{\&tau;}}(I_{\mathrm{plasma}}-I_i)---\left(2\right)$

Wherein

● G (t) is a plasma glucose concentration, and unit is mg/dl

● R _a ^Exo(t) be that the external source glucose appears at the speed (from meals or injection/infusion) in the blood plasma, unit is mg/min

● V _GBe the distribution volume of glucose, unit is dl

● S _IBe insulin sensitivity, unit is 1/min/ (μ U/ml)

● I _i(t) be a matter insulin concentration, unit is that (free the delay, a matter concentration also is lower than plasma concentration to μ U/ml, even under limit between a blood plasma and a matter insulin concentration; In these equations, do not consider this difference.Thereby, to I _i(t) correct understanding should be the ratio that the matter insulin concentration multiply by matter insulin between basic plasma insulin/basis between reality when time t)

● G _BasalBe basic plasma glucose concentration, unit is mg/dl

● I _BasalBe basic plasma insulin concentration, unit is μ U/ml

● τ is transferred to the relevant time constant of interstitial fluid with insulin from blood plasma, and unit is min

● I _PlasmaBe plasma insulin concentration, unit is μ U/ml.

$\left(\begin{array}{c}G\left(t_2\right)-G\left(t_1\right)\\ G\left(t_3\right)-G\left(t_2\right)+0.9a_{23}\\ G\left(t_4\right)-G\left(t_3\right)+0.9a_{34}\\ .\\ .\\ .\end{array}\right)=\left(\begin{array}{cc}-{\mathrm{\&Phi;}}_{12}& G_{\mathrm{meal}}/V_G\\ -{\mathrm{\&Phi;}}_{23}& a_{23}\\ -{\mathrm{\&Phi;}}_{34}& a_{34}\\ .& .\\ .& .\\ .& .\end{array}\right)\left(\begin{array}{c}{S}_I\\ f_{30}\end{array}\right)---\left(3\right)$

Wherein

● t ₁, t ₂..., t _nIt is the time point of measuring glucose and insulin

● G (t ₁), G (t ₂) ... be at t ₁, t ₂... the time the plasma glucose value

● G _MealIt is the glucose total amount that is absorbed in the feed

● a ₂₃, a ₃₄... be based on described proximate absorption overview and obtain

● Ф ₁₂, Ф ₂₃... be based on that described plasma glucose and insulin are measured and obtain

2. method according to claim 1, wherein said result is from obtaining at least about four to six samples.

3. method according to claim 1, wherein said result obtained during about two to four hours.

4. method according to claim 1, wherein said method are used to measure the effect of therapy to insulin sensitivity.

5. method according to claim 4, wherein said therapy are pharmacotherapy, trophotherapy or the behavior therapy.

6. method according to claim 1, wherein said method is used to measure therapeutic effect in preclinical study.

7. method according to claim 1, wherein said method develops disease or syndromic risk as prognosis with assess patient.

8. method according to claim 7, wherein said disease or syndrome are diabetes or metabolism syndrome.

9. method according to claim 1, wherein said method is used to monitor and/or adjust patient's treatment.

10. method according to claim 1, wherein said method is sent with automatic insulin and is used in combination.

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